The size and the computational load of fine-tuning large-scale pre-trained neural network are becoming two major obstacles in adopting machine learning in many applications. Continual learning (CL) can serve as a remedy through enabling knowledge-transfer across sequentially arriving tasks which relaxes the need to fine-tune all network weights from scratch. However, existing CL algorithms primarily consider learning unimodal vision-only or language-only tasks. We develop a transformer-based CL architecture for learning bimodal vision-and-language tasks based on increasing the number of the learnable parameters dynamically and using knowledge distillation. The new additional parameters are used to specialize the network for each task. Our approach enables sharing information between the tasks while addressing the challenge of catastrophic forgetting. Our approach is scalable learning to a large number of tasks because it requires little memory and time overhead. Our model reaches state-of-the-art performance on challenging vision-and-language tasks.